Advertisement

The European Physical Journal Special Topics

, Volume 216, Issue 1, pp 73–81 | Cite as

Maximal entropy random walk in community detection

  • J.K. OchabEmail author
  • Z. BurdaEmail author
Regular Article

Abstract

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study en- compasses the use of a stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare the performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as to significant deterioration.

Keywords

Random Walk European Physical Journal Special Topic Community Detection Stochastic Matrix Cayley Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Fortunato, Phys. Rep. 486, 75 (2010)CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Z. Burda, J. Duda, J.M. Luck, B. Waclaw, Phys. Rev. Lett. 102, 160602 (2009)CrossRefADSGoogle Scholar
  3. 3.
    Z. Burda, J. Duda, J.M. Luck, B. Waclaw, Acta Phys. Pol. B 41, 949 (2010)MathSciNetGoogle Scholar
  4. 4.
    B. Waclaw, Generic Random Walk and Maximal Entropy Random Walk, Wolfram Demonstration ProjectGoogle Scholar
  5. 5.
    J.K. Ochab, Z. Burda, Phys. Rev. E 85, 021145 (2012)CrossRefADSGoogle Scholar
  6. 6.
    J.K. Ochab, Stationary States of Maximal Entropy Random Walk and Generic Random Walk on Cayley trees, Wolfram Demonstration ProjectGoogle Scholar
  7. 7.
    J.K. Ochab,Dynamics of Maximal Entropy Random Walk and Generic Random Walk on Cayley trees, Wolfram Demonstration ProjectGoogle Scholar
  8. 8.
    J.K. Ochab, Acta Phys. Pol. B 43, 1143 (2012)CrossRefGoogle Scholar
  9. 9.
    J.H. Hetherington, Phys. Rev. A 30, 2713 (1984)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    L. Demetrius, V.M. Gundlach, G. Ochs, Theor. Popul. Biol. 65, 211 (2004)CrossRefzbMATHGoogle Scholar
  11. 11.
    L. Demetrius, T. Manke, Phys. A 346, 682 (2005)CrossRefGoogle Scholar
  12. 12.
    V. Zlatic, A. Gabrielli, G. Caldarelli, Phys. Rev. E 82, 066109 (2010)CrossRefADSGoogle Scholar
  13. 13.
    J.-C. Delvenne, A.-S. Libert, Phys. Rev. E 83, 046117 (2011)CrossRefADSGoogle Scholar
  14. 14.
    R. Sinatra, J. Gómez-Gardeñes, R. Lambiotte, V. Nicosia, V. Latora, Phys. Rev. E 83, 030103 (2011)CrossRefADSGoogle Scholar
  15. 15.
    C. Monthus, T. Garel, J. Phys. A: Math. Theor. 44, 085001 (2011)CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    K. Anand, G. Bianconi, S. Severini, Phys. Rev. E 83, 036109 (2011)CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    W. Parry, Trans. Amer. Math. Soc. 112, 55 (1964)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    S. White, P. Smyth, KDD ’03: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, 2003 (ACM, New York, USA, 2003), p. 266Google Scholar
  19. 19.
    D. Harel, Y. Koren, FST TCS ’01: Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science (Springer-Verlag, London, UK, 2001), p. 18Google Scholar
  20. 20.
    M. Latapy, P. Pons, Lect. Notes Comput. Sci. 3733, 284 (2005)CrossRefGoogle Scholar
  21. 21.
    H. Zhou, Phys. Rev. E 67, 061901 (2003)CrossRefADSGoogle Scholar
  22. 22.
    H. Zhou, Phys. Rev. E 67, 041908 (2003)CrossRefADSGoogle Scholar
  23. 23.
    H. Zhou, R. Lipowsky, Lect. Notes Comput. Sci. 3038, 1062 (2004)CrossRefGoogle Scholar
  24. 24.
    J.G. Kemeny, J.L. Snell, Finite Markov Chains (Springer Verlag, New York, 1976)Google Scholar
  25. 25.
    C.M. Grinstead, J.L. Snell, Introduction to Probability (American Mathematical Society, Providence, RI, 1997)Google Scholar
  26. 26.
    J.K. Ochab, Phys. Rev. E 86, 066109 (2012)CrossRefADSGoogle Scholar
  27. 27.
    L. Donetti, M.A. Munoz, J. Stat. Mech., P10012 (2004)Google Scholar
  28. 28.
    K.A. Eriksen, I. Simonsen, S. Maslov, K. Sneppen, Phys. Rev. Lett. 90, 148701 (2003)CrossRefADSGoogle Scholar
  29. 29.
    I. Simonsen, Phys. A 357, 317 (2005)CrossRefMathSciNetGoogle Scholar
  30. 30.
    J. Shi, J. Malik, IEEE Trans. Pattern Anal. Mach. Intell. 22, 888 (2000)CrossRefGoogle Scholar
  31. 31.
    M. Meila, J. Shi, AI and STATISTICS (AISTATS) (2001)Google Scholar
  32. 32.
    A. Capocci, V.D.P. Servedio, G. Caldarelli, F. Colaiori, Phys. A 352, 669 (2005)CrossRefGoogle Scholar
  33. 33.
    E. Estrada, N. Hatano, Phys. Rev. E 77, 036111 (2008)CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    E. Estrada, N. Hatano, Appl. Math. Comput. 214, 500 (2009)CrossRefzbMATHGoogle Scholar
  35. 35.
    M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004)CrossRefADSGoogle Scholar
  36. 36.
    A. Lancichinetti, S. Fortunato, F. Radicchi, Phys. Rev. E 78, 046110 (2008)CrossRefADSGoogle Scholar
  37. 37.
    A. Lancichinetti, S. Fortunato, Phys. Rev. E 80, 056117 (2009)CrossRefADSGoogle Scholar
  38. 38.
    L. Danon, A. Díaz-Guilera, J. Duch, A. Arenas, J. Stat. Mech.: Theory Exp., P09008 (2005)Google Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center Jagiellonian UniversityKrakówPoland

Personalised recommendations